A moving object is represented as a vector, which has an orientation and a magnitude. In order to reach exact information about the location of the moving object in a three-dimensional space at any time it is necessary to know three-dimensional vector representation of the object with respect to a reference point. When the magnitude of the relevant vector component in any axis corresponds to the acceleration of the moving object in that axis, its orientation information is obtained from the angular rate information collected by gyroscopes, which have a scale factor in terms of (°/s)/mV, based on Sagnac Effect, along with precise clock determining a time interval Δt and the voltage difference from the zero rotation voltage within Δt. As a result the orientation of any rotating frame, on which a gyroscope is mounted, is tracked by integrating the voltage differences produced from the rotation rate signal in three dimensional (x, y, z) in Δt. The angular orientation error of the rotating frame is primarily determined by inherently unpredictable optical drift which is resulted from nonlinearities of optical fiber used as sensing coil of an IFOG, which is a ring interferometer, and environmental influences such as magnetic field, and the temperature and acoustic gradients on the sensing coil caused by thermal transients, which causes the growth of angular orientation error proportional to time due to the integration process.
The first ring interferometer and the first experiment relating to light propagation in a rotation media were performed by F. Harress [1]. His experimental setup was composed of light source, readout optics, and series of rotating prisms forming a circular optical path. However, Harress couldn't have observed the effect of the rotation on the travelling light, which he had expected, due to the fact that the light source and detection system located at the middle of his setup were not undergoing rotation applied by Harress. The first successful experiment of the ring interferometer configured to observe the rotation effect proposed by G. Sagnac in 1913, which states that an optical path difference is experienced by light beams propagating along opposite directions in a rotating frame, was carried out by A. A. Michelson and H. G. Gale with a gigantic Michelson interferometer configuration in 1925. The measurement of this optical path difference is proportional to absolute rotation rate and this is a basis for all types of the optical gyroscopes. For two continuous light waves propagating in opposite directions of the media of gyroscope, SPS is a function of absolute rotation rate, (°/h). With development of optical fiber manufacturing technology, a fiber ring interferometer with multiple optical paths was first constructed by V. Vali and R. W. Shorthill in 1976 to show SPS and this fiber ring interferometer configuration is known as a pioneering step in the applications of optical fiber gyroscope.
SPS φR, which is a function of the rotation rate (angular rate) of a fiber ring interferometer with respect to an inertial frame, is only induced by rotation, not linear acceleration. φR for a fiber ring interferometer having N turn optical path is given in the following;
                              ∅          R                =                                            8              ⁢                                                          ⁢              π              ⁢                                                          ⁢              N                                                      λ                0                            ⁢                              c                0                                              ⁢                      A            ·            Ω                    ⁢                                          ⁢                                    (              ∘                        )                                              (        1        )            Where both A and Ω are vector quantities. A is the area of the enclosed optical path, Ω is the rotation rate of the two beam interferometer, λ0 and c0 is wavelength and light velocity in vacuum. Sagnac Effect in matter is more delicate to explain, but it is completely independent of the indices of refraction or of the guidance condition, and keeps the same value as that in the vacuum. If the optical path in the gyroscope configuration consists of N turns, i.e., optical fiber, SPS (∅R) is given as in Eq.(1) [1]. The fiber ring interferometer, now to be called as Interferometric Fiber Optic Gyroscope (IFOG) herein, has a cosine response in Eq.(2).I=ηP0(1+cos ∅R) (A)  (2)Where I is total photodiode current defining the interferometer response in A, η is the spectral responsivity of the photodiode in A/W, and P0 is optical power falling onto photodiode in W. It is very hard to observe and extract the SPS from Eq.(2) in DC signal methods. For extracting SPS and enhancing the signal to noise ratio, a reciprocal phase modulation is applied to optical path in which the counter propagating light waves at clockwise (CW) and counter clockwise (CCW) by periodically modulating sine and square waves, the amplitudes and the angular frequencies of which hold the ring interferometer's sensitivity at ±π/2 rad.I=ηP0(1+cos ∅R+Δ∅m(t)) (A)  (3)Sine-reciprocal phase modulation Δ∅m(t) for propagation of CW and CCW lightwaves inside the optical fiber of the sensing coil, in which the travelling time of light is τg for a light velocity in vacuum, is,Δ∅m(t)=∅cw−∅ccw=∅b0 sin ωmt  (4)Δ∅m(t)=∝·Vmodp-p·{sin ωmt−sin ωm(t−τg)}=∅cw−∅ccw  (5)There is a retardation of τg between the arms of the sensing coil to which the phase modulation is applied and not applied. By using the trigonometric identities Eq.(6) is obtained.
                              Δ          ⁢                                          ⁢                                    ∅              m                        ⁡                          (              t              )                                      =                  2          ⁢                                          ⁢                      ∅                          b              ⁢                                                          ⁢              0                                ⁢          sin          ⁢                                                    ω                m                            ⁢                              τ                g                                      2                    ⁢          cos          ⁢                                          ⁢                                    ω              m                        ⁡                          (                              t                -                                                      τ                    g                                    2                                            )                                                          (        6        )            Where
      ∅          b      ⁢                          ⁢      0        =                    2        ⁢        π        ⁢                                  ⁢        Δ        ⁢                                  ⁢        L        ⁢                                  ⁢        Δ        ⁢                                  ⁢        n            λ        =                  ∝                  ·                      V            mod                          p              -              p                                          =                        ±          π                ⁢                  /                ⁢        2        ⁢                                  ⁢        for        ⁢                                  ⁢                  f          m                ⁢        1        ⁢                  /                ⁢        2        ⁢                              τ            g                    .                    Vmodp-p is the amplitude of modulation voltage, ∝ is the voltage-phase conversion factor of phase modulator in (°/mV), ∅b0 is the amplitude of the phase created inside the sensing coil, ΔL is the length difference of sensing coil to which the phase modulation is applied, Δn is the refractive index difference taking places on relevant crystal axis of the electro-optic modulator against the applied modulation voltage Vmodp-p, and fm is the frequency of function generator applying phase modulation to phase modulator in Hz. A low coherent source in the sensing coil of IFOG interfere with each other at the middle of the coil and the standing wave contrasted by means of the phase modulation applied forms within this restricted length of the optical fiber, which is temporal coherence length, Lc [2]. The term τg/2 in Eq.(6) shows this point. Eq.(6) can be rearranged as in Eq.(7)Δ∅m(t)=∅b cos ωmt  (7)Where
          ⁢            ∅      b        =          2      ⁢                          ⁢              ∅                  b          ⁢                                          ⁢          0                    ⁢      sin      ⁢                                    ω            m                    ⁢                      τ            g                          2            and by writing
  t  →      (          t      -                        τ          g                2              )  in Eq.(6). By using the Jacobi-Anger series expansion in terms of 1st Kind Bessel Functions, the photocurrent stated in Eq.(3), the Eq.(8) is derived in terms of even and odd frequencies harmonics of the sine modulation applied to phase modulator.I=ηP0{1+(J0(∅b)+2J2(∅b)cos 2ωmt . . . )cos ∅R+(2J1(∅b)cos ωmt+2J3(∅b)cos 3ωmt+ . . . )sin ∅R}   (8)For the first harmonics, after passing through the band pass filter of the demodulation circuit of IFOG, the photodiode current for fm=½τg is Iωm,Iωm=2ηP0J1(∅b)sin ∅R (A)  (9)For square wave modulation, the form of Eq.(9) is given in Eq.(10) [3].Iωmsquare=2ηP0 sin ∅b sin ∅R (A)  (10)With the modulation frequency of fm=, ½τg, Vmodp-p is so determined that ∅b makes the photodiode current maximum by taking voltage-phase conversion factor of phase modulator (∝, °/mV) into account [4]. ∅b values making the photodiode current maximum are 1.8 rad for sine modulation type and π/2 rad for square wave modulation. When compared the square wave response with sine wave response, the square wave response is higher than that of sine wave response as “1/0.53”. The demodulation voltage VGyro_Coil(Ω) produced by photodiode current for sine wave modulation. “Gyro Coil” has a length of 1700 m, corresponding to τg=8.57 μs.VGyro_Coil(∅RGyro_Coil)=2ηP0TFGJ1(∅b)sin(∅RGyro_Coil) (V)  (11)Where TF is transfer function of current-to-voltage converter in (V/A) and G characterizes the gain and ohmic loss of the demodulation circuit. The optical power P0 includes all the optical loss in the IFOG circuit due to fusion splices, mating sleeves and MEMS FO ON/OFF switches. Eq.(11) can be written in the most general form as Eq.(12), regardless of square wave or sine wave response. The term 2ηP0 TF G J1(∅b) will be called as A1,j in the next sections.VGyro_Coil(∅RGyro_Coil)=A1 sin(A2·Ω+A3)+A4 (V)  (12)Where,A1=2ηP0 TF G J1(∅b), electrical scale factor, (mV)
            A      2        =                            8          ⁢                                          ⁢          π          ⁢                                          ⁢          N                                      λ            0                    ⁢                      c            0                              ⁢              A        GC              ,optical scale factor of IFOG sensing coil, (sec). ∅RGyro_Coil=A2·ΩA3=∅d_optGyro_Coil=√{square root over (∅faraday2+∅shupe2+∅kerr2)}, optical drift parameter of IFOG sensing coil at any time, (°)A4=∅d_electGyro_Coil, electrical drift of IFOG at any time t, (mV) [5 and 6].With the use of the IFOG having a demodulation output, the total angular displacement Dj, (also called as Tracking Orientation) is calculated Eq.(13) within time interval of Δt. Subscript j shows the time domain running with a developed software for this invention to be referred as “The software_2” in Description section when the DDM-IFOG in its normal operation, sensing the yaw rotation.Dj(ΔΩj)=ΣjΔΩj·Δtj(°)  (13)ΔΩ=SF·ΔV(°/h)  (14)Where SF is scale factor of IFOG. For open loop IFOG, SFopen=|Ω|/VGyro_Coil [7] and for closed loop IFOG
            SF      closed        =                  [                                                            λ                0                            ⁢                              c                0                                                    8              ⁢              π              ⁢                                                          ⁢              NA                                ⁢                      ∅            fb                          ]                    [                  V                      phase            ⁢                                                  ⁢            _            ⁢                                                  ⁢            zeroing                          ]              ,∅fb=∝Vphase_zeroing, [4]. The unit of scale factor is (°/h)/mV. The scale factor of open loop IFOG is not linear due to sine function in VGyro_Coil whereas the scale factor of closed loop IFOG is nearly flat [4]. Total instantaneous angular displacement Dj can be written in terms of instantaneous SPS as followsDj(∅R,jGyro_Coil)=SFΣjΔVj·Δtj(°)  (15)ΔVj={[A1,j sin(∅R,jGyro_Coil+∅d_opt,jGyro_Coil)+∅d_electGyro_Coil]−A10[sin(∅d_opt0_Gyro_Coil)+∅d_elect0_Gyro_Coil]}   (16)Where A10 and A1,j is the electrical scale factor of the demodulation circuit of the IFOG having “Gyro Coil” at initial time defined as t=0 and any instantaneous time t, respectively. ∅d_opt,j0_Gyro_Coil and ∅d_elect0_Gyro_Coil represent the instantaneous optical drift of the IFOG's sensing coil, and the electrical drift of the demodulation circuit of IFOG at initial time, respectively. The variation on A1,j sin(∅R,jGyro_Coil+∅d_opt,jGyro_Coil) is called as the drift of an IFOG when ∅R,jGyro_Coil=0·ΔVj is the instantaneous net voltage difference between zero rotation rate voltage of the demodulation circuit and SPS induced-voltage generated by the demodulation circuit. The electrical drift of the demodulation circuit manufactured with high quality active and passive electronic components together with the optical intensity stabilization of low coherent source, which the low coherence reduces the excess noise and backscattering noise effects causing random walk but dynamic range, is such small that it can be neglected as compared with the optical drift component. With good grounding and guarding practices on the demodulation circuit, it can be assumed that ∅d_elect0_Gyro_Coil at initial time is equal to ∅d_electGyro_Coil at any time t. Final form of Eq.(16) is,ΔVj={[A1,j sin(∅R,jGyro_Coil+∅d_opt,jGyro_Coil)]−[A10 sin(∅d_opt0_Gyro_Coil)]}(V)  (17)If the Eq.(15) is re-arranged again by using Eq.(17) for the angular displacement of the yaw axis (z-axis) rotation within the time interval of Δt,Djyaw(∅R,jGyro_Coil)=SFΣj{A1,j sin(∅R,jGyro_Coil+∅d_opt,jGyro_Coil)−A10 sin(∅d_opt0_Gyro_Coil)}·Δtj(°)   (18)Allan Variance, a time domain analysis, is implemented for the systems influenced by noise. The uncertainty in the useful data obtained from the system, is generated by the random errors caused by noisy effects. Hence the contribution of the variance of any noise source is calculated or estimated by the voltage data obtained under the absence of stimulating effect, such as angular rate for gyroscope. ∅d_opt,jGyro_Coil and A1,j are not static and have randomly changing behavior (dynamic behavior) in time. ∅d_opt0_Gyro_Coil is a static value together with A10 Resultantly, the variance between A1,j sin(∅d_opt,jGyro_Coil) and A10 sin(∅d_opt0_Gyro_Coil) is determined by Allan Variance, which is primarily defined and characterized before the IFOG is not put into operation. That ∅d_opt,jGyro_Coil is equal to ∅d_opt0_Gyro_Coil means no optical drift but in realistic world, ∅d_opt,jGyro_Coil≠∅d_opt0_Gyro_Coil and A1,j≠A10 due to random noise variables influencing on the sensing coil, and the optical emission source. In brief, the instantaneous drift of the IFOG runs in random behavior. The drift of an IFOG is the average output obtained from the demodulation circuit (total phase zeroing voltages applied to phase modulator, regardless of type of phase modulator, for closed loop IFOG) in °/h, when IFOG is not undergoing any influence of angular rate. Resultantly the drift resulted from random variation among the optical drift parameters ∅d_opt,jGyro_Coil and ∅d_opt0_Gyro_Coil and the variation on A1,j causes to grow the error at the angular displacement with time proportionally because of the integration in Eq. (18).The drift of the IFOG, to be referred as the instantaneous drift herein, is fully composed of the optical drift ∅d_opt,jGyro_Coil and the drift (variation) on A1,j.
Additional knowledge necessary for achieving this invention which concerns with the scale factor determinations of open-loop and closed-loop type IFOGs, the demodulation circuit characterizations with respect to the angular rate projections on the relevant latitudes, and the influences of polarization effects propagating inside the sensing coils along with manufacturing and winding process of the optical fiber comprising the sensing coil on the optical drift of an IFOG, which are the vital topics often addressed, was deeply investigated and introduced in [6, 7, 8, and 9].
Regarding the most related international patents still in progress to the presented invention;
The pioneering step in construction of a fiber ring interferometer was the study proposed in the East-Coast Conference of the SPIE in Reston, Va. by Vali et al. on March 22 and 23 of 1976 but this study is non-patented. The presented invention described in this text contains software supported-structural modifications to monitor and derive the instantaneous drift, directly corresponding to the zero rotation rate voltage of the demodulation circuit of the DDM-IFOG with “Gyro Coil”, the sensitive surface vector of which is placed parallel to z-axis (yaw axis) as in FIG. 1, under the influence of continuous yaw rotation rate on the reduced IFOG configuration patented as “Reduced minimum configuration interferometric fiber optic gyroscope with simplified signal processing electronics”, the patent number of which is U.S. Pat. No. 6,351,310 (B1).
According to US 2011126647, this patent disclosure, US2011126647 (A1), deals with the drift compensation MEMS (Micro-Electro-Mechanical Structure) gyroscopes. In the method presented in US 2011126647 (A1), MEMS gyroscope is sequentially oriented to the first and the second orientations, inverted as 180°, relative to each other by a motor which generates a rotation of 180°. Then the unpredicted drift of MEMS-based gyroscope is determined by comparing two signals. The presented invention differs from the invention disclosure in US2011126647 (A1) in that the following aspects: the invention presented as a novel Interferometric Fiber Optic Gyroscope (IFOG) and the method is related to monitoring and determining the instantaneous drift of IFOG under continuous yaw rotation without disturbing the current orientation of the sensing coil of the IFOG configuration invented. Instead of the sequentially and/or periodically re-orienting the sensing coil, “Gyro Coil” on z-axis (yaw axis) in the presented invention, a secondary fiber coil “Monitor Coil” on x-axis (pitch axis) is used by switching both of the coils through MEMS FO ON/OFF switches.
Furthermore, the method, which is subjected to compensating the inherent drift of gyroscope, introduced in WO2010114915 (A2) covers the transfer of the heuristic assumptions to the accumulator circuit, such as swaying, curving or turning, for slowly-varying drift errors by means of a feedback loop control. The presented invention doesn't contain any heuristic assumption to monitor, derive, and compensate the unpredictable drift of the IFOG in real time. The presented invention is fully different from WO2010114915 (A2).